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If A and B are two square matrices such that B=−A−1BA then A+B2=

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a

0

b

A2+B2

c

A2+2AB+B2

d

A+B

answer is B.

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Detailed Solution

B=A−1BA⇒AB=−AA−1BA =−BA(A+B)2=(A+B)(A+B) =A(A+B)+B(A+B)=A2+AB+BA+B2=A2+B2

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